On the harmonic index and algebraic connectivity

期刊论文
发表日期：

2024年5月16日

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S. M. Sheikholeslami,
H. Shooshtari

摘要

The harmonic index of a graph G is defined as the sum of weights $\frac{2}{d_i+d_j}$ $\frac{2}{d_{i} + d_{j}}$ over all edges $v_iv_j$ $v_{i} v_{j}$ of G, where $d_i$ $d_{i}$ and $d_j$ $d_{j}$ are the degrees of the vertices $v_i$ $v_{i}$ and $v_j$ $v_{j}$ in G, respectively. In this paper we resolve a conjecture, obtained by the AutoGraphiX system, about the relation between the harmonic index and the algebraic connectivity of graphs.